The terms “reconstitute” and “rehydrate” are usually used interchangeably in food language, and that’s usually fine, as there’s only a slight difference in meaning. Both mean to add liquid to something.
When you rehydrate something, that something is generally considered to be “dehydrated”, as in all the water is gone out of it: powdered milk, dried mushrooms, etc.
When you reconstitute something, the something that you are adding liquid back to may not be “dehydrated”, as in all the water being gone — it may have just some of the water gone, making it condensed or concentrated food.
So, while you rehydrate powdered milk, you wouldn’t say in English that you are rehydrating frozen orange juice — you are “just” reconstituting it, because it was never completely missing all its water.
To reconstitute foods, you just add a liquid and stir.
To rehydrate foods, such as powdered milk, you can just stir. Others, such as dried onions, mushrooms and glass noodles, have to soak in water for a period of time. You can speed the soaking process up by using boiling water.